This has already been added to the game as one of the easiest enchantments to get (you can get it on a helmet or book enchanted at level 1):
Increases underwater mining rate.
Breaking blocks underwater is allowed at regular speed, though the player cannot be floating to get the full effect. Specifically, when swimming, mining takes 5X as long. Levels above 1 are no different.
Yup, with Aqua Affinity on your helmet and Depth Strider III on your boots you can mine very fast underwater. Adding Respiration III to the helmet will allow your air supply to last longer so you won't have to catch your breath as often or use potions. With that and a well enchanted shovel you can sprint underwater and mow down rows of gravel or sand.